...1981) uses the terms "translation" and "elementary translation", and both "principal" and "elementary" are found in the literature. [[User:Richard Pinch|Richar
396 bytes (53 words) - 08:16, 2 September 2017
...of the indicatrix of the curvature (cf. [[Dupin indicatrix]]). If $t$ is a principal direction, the relation (Rodrigues' formula)
...l direction. The normal curvature in a principal direction is known as a [[principal curvature]].
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$#C+1 = 45 : ~/encyclopedia/old_files/data/P074/P.0704660 Principal curvature
...direction, i.e. in a direction in which it assumes an extremal value. The principal curvatures $ k _ {1} $
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The left principal ideal $L(\alpha)$ of a ring $A$ contains, in addition to the element $\alph
the right principal ideal $R(\alpha)$ contains all the elements
3 KB (484 words) - 20:54, 28 November 2014
''Dirichlet principal character''
where $D$ is a given natural number. Principal characters serve to define the concepts of primitive and imprimitive charac
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...scending chains of normal subgroups have finite length. If a group has two principal series, then they are isomorphic, i.e. they have the same length and there
The terminology "principal series" is almost never used in the West. Instead one uses chief series. T
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-
557 bytes (88 words) - 16:59, 23 November 2023
...ity $A^2=A$ is valid. All [[regular semi-group]]s are semi-simple. If each principal factor of a semi-group is either completely $0$-simple or completely simple
Any semi-group consists, as it were, of its principal factors. This explains, in particular, the important role played by ideally
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-
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...principal [[ultrafilter]]. The [[Fréchet filter]] is an example of a non-principal filter.
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$#C+1 = 9 : ~/encyclopedia/old_files/data/P074/P.0704750 Principal normal
is the parametric equation of the curve and the value $ t _ {0} $
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A [[Principal G-object|principal $ G $-
then a principal $ G $-
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$#C+1 = 75 : ~/encyclopedia/old_files/data/P074/P.0704690 Principal fibre bundle
The significance of principal fibre bundles lies in the fact that they make it possible to construct asso
6 KB (847 words) - 20:45, 12 January 2024
...ure Lie group acts simply transitively and analytically. In other words, a principal analytic fibration is a quadruple $ (P,\ B,\ G,\ \pi ) $
dimensional fibre determines a principal analytic fibration with base $ B $
7 KB (1,096 words) - 09:58, 20 December 2019
$#C+1 = 81 : ~/encyclopedia/old_files/data/P074/P.0704740 Principal ideal ring
...[[Associative rings and algebras]]) in which all right and left ideals are principal, i.e. have the form $ aR $
5 KB (880 words) - 19:00, 9 January 2024
$#C+1 = 99 : ~/encyclopedia/old_files/data/P074/P.0704710 Principal \BMI G\EMI\AAhobject
...ndle|principal fibre bundle]] in topology, a [[Principal homogeneous space|principal homogeneous space]] in algebraic geometry, etc. Let $ G $
6 KB (908 words) - 16:33, 7 June 2020
...th boundary, then they can be extended to the entire space $E^n$ so that a principal fundamental solution will exist for the extended operator.
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#REDIRECT [[Principal ideal ring]]
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...ves as the base of two different deformations $F'$ and $F''$, then it is a principal base of deformation.
...normal curvature of $F$ in the direction of one of the two families of the principal base $\sigma$ at an arbitrary point $M\in F$, while $\kappa'$, $\kappa''$,
5 KB (766 words) - 12:40, 2 November 2014
$#C+1 = 14 : ~/encyclopedia/old_files/data/M062/M.0602310 Mapping, principal net of a,
The directions tangential to the lines of the principal net of the mapping at the point $ x \in G $
1 KB (229 words) - 07:59, 6 June 2020
$#C+1 = 26 : ~/encyclopedia/old_files/data/P074/P.0704790 Principal type, partial differential operator of,
whose principal part $ P( D) $(
2 KB (356 words) - 08:07, 6 June 2020
...discarding all the terms not containing derivatives of maximal order. The principal part of the differential operator
...differentiations with respect to the various arguments. For instance, the principal part of the differential operator $D_1-D_2^2+\alpha D_2$ is sometimes defin
2 KB (249 words) - 14:26, 8 August 2014
This page is a copy of the article [[Principal analytic fibration]] in order to test [[User:Maximilian_Janisch/latexlist|a
...ure Lie group acts simply transitively and analytically. In other words, a principal analytic fibration is a quadruple $( P , B , G , \pi )$ where $P$ and $B$ a
8 KB (1,155 words) - 13:44, 17 October 2019
This page is a copy of the article [[Principal homogeneous space]] in order to test [[User:Maximilian_Janisch/latexlist|au
...gy]] $H ^ { 1 } ( k , \Gamma )$. In the general case the set of classes of principal homogeneous spaces over an $5$-group scheme $I$ coincides with the set of o
5 KB (863 words) - 13:44, 17 October 2019
...the normal curvature of a surface in a given direction $l$ in terms of the principal curvatures $k_1$ and $k_2$:
...between the direction $l$ and the principal direction corresponding to the principal curvature $k_1$.
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...l space of a [[bundle]], transforming the latter into a [[Bundle#principal|principal $G$-bundle]].
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...of the indicatrix of the curvature (cf. [[Dupin indicatrix]]). If $t$ is a principal direction, the relation (Rodrigues' formula)
...l direction. The normal curvature in a principal direction is known as a [[principal curvature]].
1 KB (180 words) - 16:49, 12 October 2017
...principal [[ultrafilter]]. The [[Fréchet filter]] is an example of a non-principal filter.
454 bytes (69 words) - 12:00, 23 November 2023
...discarding all the terms not containing derivatives of maximal order. The principal part of the differential operator
...differentiations with respect to the various arguments. For instance, the principal part of the differential operator $D_1-D_2^2+\alpha D_2$ is sometimes defin
2 KB (249 words) - 14:26, 8 August 2014
...by K.M. Peterson as examples of surfaces allowing of a deformation over a principal base.
827 bytes (119 words) - 17:12, 7 February 2011
...onversely (Finikov's theorem), the only surface with an infinite number of principal bases is a right helicoid [[#References|[2]]].
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''Dirichlet principal character''
where $D$ is a given natural number. Principal characters serve to define the concepts of primitive and imprimitive charac
340 bytes (45 words) - 20:04, 9 January 2015
#REDIRECT [[Principal translation]]
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#REDIRECT [[Principal ideal ring]]
34 bytes (4 words) - 20:26, 7 February 2017
...ly for principal ideals) which is Bezout is a principal ideal ring. As for principal ideal rings, a module of finite type over a Bezout ring is a direct sum of
1 KB (190 words) - 19:52, 2 November 2014
...equal to zero, one of the principal curvatures (cf. [[Principal curvature|Principal curvature]]) vanishes, and the coefficients of the [[Second fundamental for
924 bytes (123 words) - 19:11, 12 April 2014
...1981) uses the terms "translation" and "elementary translation", and both "principal" and "elementary" are found in the literature. [[User:Richard Pinch|Richar
396 bytes (53 words) - 08:16, 2 September 2017
...that generates a prime ideal). An atomic [[Bezout ring|Bezout ring]] is a principal ideal ring.
...one simply speaks of rings which satisfy the ascending chain condition for principal ideals or the divisor chain condition.
1 KB (177 words) - 17:14, 7 February 2011
$#C+1 = 14 : ~/encyclopedia/old_files/data/M062/M.0602310 Mapping, principal net of a,
The directions tangential to the lines of the principal net of the mapping at the point $ x \in G $
1 KB (229 words) - 07:59, 6 June 2020
...states that $b^G$ is the principal block of $RG$ if and only if $b$ is the principal block of $RH$.
1 KB (249 words) - 09:15, 27 June 2014
$#C+1 = 26 : ~/encyclopedia/old_files/data/P074/P.0704790 Principal type, partial differential operator of,
whose principal part $ P( D) $(
2 KB (356 words) - 08:07, 6 June 2020
...ity $A^2=A$ is valid. All [[regular semi-group]]s are semi-simple. If each principal factor of a semi-group is either completely $0$-simple or completely simple
Any semi-group consists, as it were, of its principal factors. This explains, in particular, the important role played by ideally
2 KB (362 words) - 19:18, 16 January 2018
...and vice versa. If $\sigma$ is a principal base for a [[Deformation over a principal base|deformation]] of $X$, then $Y$ is a [[Bianchi surface]].
468 bytes (76 words) - 19:44, 24 April 2016
...f it is closed with respect to all translations (or with respect to merely principal translations).
759 bytes (110 words) - 16:59, 23 November 2023
...ase|deformation over a principal base]] and to classify them. Thus, if the principal base contains two families of geodesic lines, the functions $U$ and $V$ are
...ss $B_1$ is characterized by the fact that only one family of lines of the principal base are geodesics (one of the functions $U,V$ is constant); conoids may se
2 KB (294 words) - 14:19, 29 April 2014
...element of $S$, and similarly the left [[annihilator]] of any element is a principal left ideal on an idempotent element of $S$.
714 bytes (106 words) - 16:43, 23 November 2023
The left principal ideal $L(\alpha)$ of a ring $A$ contains, in addition to the element $\alph
the right principal ideal $R(\alpha)$ contains all the elements
3 KB (484 words) - 20:54, 28 November 2014
...ves as the base of two different deformations $F'$ and $F''$, then it is a principal base of deformation.
...normal curvature of $F$ in the direction of one of the two families of the principal base $\sigma$ at an arbitrary point $M\in F$, while $\kappa'$, $\kappa''$,
5 KB (766 words) - 12:40, 2 November 2014
''
principal series of representations''
...images/c/c025/c025750/c0257507.png" />, then the non-degenerate continuous
principal series of representations of <img align="absmiddle" border="0" src="https:/
8 KB (1,022 words) - 17:01, 7 February 2011
A [[Principal G-object|principal $ G $-
then a principal $ G $-
5 KB (854 words) - 10:51, 20 December 2019
This page is a copy of the article [[Principal homogeneous space]] in order to test [[User:Maximilian_Janisch/latexlist|au
...gy]] $H ^ { 1 } ( k , \Gamma )$. In the general case the set of classes of principal homogeneous spaces over an $5$-group scheme $I$ coincides with the set of o
5 KB (863 words) - 13:44, 17 October 2019
...y less than $\mathfrak{a}$. The Fréchet filter is not [[principal filter|principal]].
812 bytes (126 words) - 16:20, 18 November 2023
$#C+1 = 81 : ~/encyclopedia/old_files/data/P074/P.0704740 Principal ideal ring
...[[Associative rings and algebras]]) in which all right and left ideals are principal, i.e. have the form $ aR $
5 KB (880 words) - 19:00, 9 January 2024
$#C+1 = 99 : ~/encyclopedia/old_files/data/P074/P.0704710 Principal \BMI G\EMI\AAhobject
...ndle|principal fibre bundle]] in topology, a [[Principal homogeneous space|principal homogeneous space]] in algebraic geometry, etc. Let $ G $
6 KB (908 words) - 16:33, 7 June 2020
[[Principal fibre bundle|principal fibre bundle]] the existence of a section implies its triviality. A
704 bytes (110 words) - 22:27, 24 November 2013
...ere $k_i$ is the principal curvature at a point on the hypersurface in the principal direction $i$.
2 KB (369 words) - 21:48, 1 January 2019
...ipal ideal ring is factorial. A Dedekind ring is factorial only if it is a principal ideal ring. If $S$ is a multiplicative system in a factorial ring $A$, then
3 KB (480 words) - 21:45, 3 January 2021
...a Voss net is isotropic. Every Voss net on a two-dimensional surface is a principal base of a deformation of the surface. Only the helicoid carries an infinite
...lign="top">[2]</TD> <TD valign="top"> S.P. Finikov, "Deformation over a principal base and related problems in geometry", Vereinigt. Wiss.-Techn. Verl. 176 S
1,007 bytes (149 words) - 17:25, 31 March 2018
...ngruence (cf. [[Congruence of lines|Congruence of lines]]) with indefinite principal surfaces.
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$#C+1 = 75 : ~/encyclopedia/old_files/data/P074/P.0704690 Principal fibre bundle
The significance of principal fibre bundles lies in the fact that they make it possible to construct asso
6 KB (847 words) - 20:45, 12 January 2024
...scending chains of normal subgroups have finite length. If a group has two principal series, then they are isomorphic, i.e. they have the same length and there
The terminology "principal series" is almost never used in the West. Instead one uses chief series. T
2 KB (254 words) - 16:51, 30 December 2018
$#C+1 = 45 : ~/encyclopedia/old_files/data/P074/P.0704660 Principal curvature
...direction, i.e. in a direction in which it assumes an extremal value. The principal curvatures $ k _ {1} $
4 KB (610 words) - 14:54, 7 June 2020
$#C+1 = 9 : ~/encyclopedia/old_files/data/P074/P.0704750 Principal normal
is the parametric equation of the curve and the value $ t _ {0} $
1 KB (159 words) - 08:07, 6 June 2020
The principal linear part of increment of $Q$ under its transformation induced by the loc
...nsor, density, etc.), then the Lie differential $\delta_X Q$ describes the principal linear part of variation with time of $Q$ from the point of view of an obse
1 KB (181 words) - 19:31, 28 December 2014
...with the problem of [[Deformation over a principal base|deformation over a principal base]]. For example, there is a Peterson correspondence between a surface a
...common parametrization, then their third fundamental forms are equal. The principal net for the asymptotic nets (cf. [[Asymptotic net|Asymptotic net]]) of $
4 KB (660 words) - 19:40, 3 January 2021
Here $Q(\xi_1,\dots,\xi_n,x_1,\dots,x_n)$ is the principal symbol of the linear partial differential operator, the dot indicates diffe
are valid for at least one value of $s$, then it follows that they are valid for all values of $s$.
3 KB (419 words) - 22:32, 10 December 2018
...on the principal diagonal of $L$ will then all be equal, and their common value is the number of spanning trees of $G$. Spanning trees are employed, for ex
The number of spanning trees is a special value of the [[Tutte polynomial]] of the graph, $T_G(1,1)$.
1 KB (198 words) - 12:59, 29 December 2014
...th boundary, then they can be extended to the entire space $E^n$ so that a principal fundamental solution will exist for the extended operator.
1 KB (190 words) - 08:35, 31 October 2014
is called a principal fibre bundle with structure group $ G $.
is called a fibre bundle with structure group associated with the principal fibre bundle $ \xi $,
6 KB (989 words) - 19:40, 5 June 2020
by any of the following unit vectors: the tangent, the principal normal or the binormal of this curve. Let $ \mathbf r = \mathbf r ( s) $
that of the spherical indicatrix of the principal normal by the equation
2 KB (378 words) - 08:22, 6 June 2020
A figure consisting of the tangent, the [[Principal normal|principal normal]] and the [[Binormal|binormal]] of a space curve, and the three plan
1 KB (210 words) - 08:02, 6 June 2020
...d no subsidiary points; elements of the fourth kind contain a continuum of principal points and infinitely many subsidiary points.
...oebe [[#References|[2]]]. It is based on equivalence classes of paths. The principal theorem in the theory of prime ends is the theorem of Carathéodory: Under
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...this parabolic subgroup; this part is called the corresponding principal (principal degenerate, if the parabolic subgroup is not a Borel subgroup) series repre
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...riterion]], which reduces all calculations in it to the calculation of the principal minors of only even (or only odd) orders of a Hurwitz matrix.
...[Routh–Hurwitz criterion|Routh–Hurwitz criterion]]); let $\Delta_i$ be its principal minor of order $i$, $i=1,\dotsc,n$.
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